Why did God punish himself for the sins of man?

As far as I know, the Christian Faith is that Jesus was the son of God and God's incarnation of Himself on earth. Jesus died and suffered on the cross to account for the sins of Man, who are God's Creation. Was this because God had Created Man with flaws and realised His punishment and judgement of man for those flaws was unjust and he should take the rap for them? Does God plan to make a perfect new world where He wouldn't be judging and punishing man, for man's flaws, as is, in this world we occupy ?